Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 7.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, z, \sin y + x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) z (+ (sin y) x)))

C

double code(double x, double y, double z) {
	return fma(cos(y), z, (sin(y) + x));
}

Julia

function code(x, y, z)
	return fma(cos(y), z, Float64(sin(y) + x))
end

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * z + N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

   5. lower-fma.f64 99.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

   6. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   8. lower-+.f64 99.9

      \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-11} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.36e-11) (not (<= x 4.3e-48)))
   (* (- x) (fma (/ (* (cos y) z) x) -1.0 -1.0))
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.36e-11) || !(x <= 4.3e-48)) {
		tmp = -x * fma(((cos(y) * z) / x), -1.0, -1.0);
	} else {
		tmp = sin(y) + (z * cos(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.36e-11) || !(x <= 4.3e-48))
		tmp = Float64(Float64(-x) * fma(Float64(Float64(cos(y) * z) / x), -1.0, -1.0));
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.36e-11], N[Not[LessEqual[x, 4.3e-48]], $MachinePrecision]], N[((-x) * N[(N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] * -1.0 + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.36e-11 or 4.3e-48 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.9

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      5. sub-neg N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(-x\right) \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x} \cdot -1} + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\sin y + z \cdot \cos y}{x} \cdot -1 + \color{blue}{-1}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\mathsf{fma}\left(\frac{\sin y + z \cdot \cos y}{x}, -1, -1\right)} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}}, -1, -1\right) \]

      10. +-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{z \cdot \cos y + \sin y}}{x}, -1, -1\right) \]

      11. *-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\cos y \cdot z} + \sin y}{x}, -1, -1\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)}}{x}, -1, -1\right) \]

      13. lower-cos.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right)}{x}, -1, -1\right) \]

      14. lower-sin.f64 99.9

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right)}{x}, -1, -1\right) \]

   7. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \sin y\right)}{x}, -1, -1\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{z \cdot \cos y}{x}, -1, -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.8%

       \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right) \]

   if -1.36e-11 < x < 4.3e-48

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]
   4. Step-by-step derivation

      1. lower-sin.f64 97.1

         \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\sin y} + z \cdot \cos y \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-11} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-11} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.36e-11) (not (<= x 4.3e-48)))
   (* (- x) (fma (/ (* (cos y) z) x) -1.0 -1.0))
   (fma (cos y) z (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.36e-11) || !(x <= 4.3e-48)) {
		tmp = -x * fma(((cos(y) * z) / x), -1.0, -1.0);
	} else {
		tmp = fma(cos(y), z, sin(y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.36e-11) || !(x <= 4.3e-48))
		tmp = Float64(Float64(-x) * fma(Float64(Float64(cos(y) * z) / x), -1.0, -1.0));
	else
		tmp = fma(cos(y), z, sin(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.36e-11], N[Not[LessEqual[x, 4.3e-48]], $MachinePrecision]], N[((-x) * N[(N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] * -1.0 + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.36e-11 or 4.3e-48 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.9

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      5. sub-neg N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(-x\right) \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x} \cdot -1} + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\sin y + z \cdot \cos y}{x} \cdot -1 + \color{blue}{-1}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\mathsf{fma}\left(\frac{\sin y + z \cdot \cos y}{x}, -1, -1\right)} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}}, -1, -1\right) \]

      10. +-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{z \cdot \cos y + \sin y}}{x}, -1, -1\right) \]

      11. *-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\cos y \cdot z} + \sin y}{x}, -1, -1\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)}}{x}, -1, -1\right) \]

      13. lower-cos.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right)}{x}, -1, -1\right) \]

      14. lower-sin.f64 99.9

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right)}{x}, -1, -1\right) \]

   7. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \sin y\right)}{x}, -1, -1\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{z \cdot \cos y}{x}, -1, -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.8%

       \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right) \]

   if -1.36e-11 < x < 4.3e-48

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \sin y \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right) \]

      5. lower-sin.f64 97.1

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right) \]

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-11} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\cos y, z, \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := \left(-x\right) \cdot \mathsf{fma}\left(\frac{t\_0}{x}, -1, -1\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -520:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y + x\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (* (- x) (fma (/ t_0 x) -1.0 -1.0))))
   (if (<= z -5.3e+151)
     t_0
     (if (<= z -520.0)
       t_1
       (if (<= z 3.8e-24)
         (fma 1.0 z (+ (sin y) x))
         (if (<= z 2.05e+117) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = -x * fma((t_0 / x), -1.0, -1.0);
	double tmp;
	if (z <= -5.3e+151) {
		tmp = t_0;
	} else if (z <= -520.0) {
		tmp = t_1;
	} else if (z <= 3.8e-24) {
		tmp = fma(1.0, z, (sin(y) + x));
	} else if (z <= 2.05e+117) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = Float64(Float64(-x) * fma(Float64(t_0 / x), -1.0, -1.0))
	tmp = 0.0
	if (z <= -5.3e+151)
		tmp = t_0;
	elseif (z <= -520.0)
		tmp = t_1;
	elseif (z <= 3.8e-24)
		tmp = fma(1.0, z, Float64(sin(y) + x));
	elseif (z <= 2.05e+117)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[((-x) * N[(N[(t$95$0 / x), $MachinePrecision] * -1.0 + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+151], t$95$0, If[LessEqual[z, -520.0], t$95$1, If[LessEqual[z, 3.8e-24], N[(1.0 * z + N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+117], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.29999999999999999e151 or 2.05e117 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.8

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 93.4

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -5.29999999999999999e151 < z < -520 or 3.80000000000000026e-24 < z < 2.05e117

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.8

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)} \]

      3. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right) \]

      5. sub-neg N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(-x\right) \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x} \cdot -1} + \left(\mathsf{neg}\left(1\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\sin y + z \cdot \cos y}{x} \cdot -1 + \color{blue}{-1}\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\mathsf{fma}\left(\frac{\sin y + z \cdot \cos y}{x}, -1, -1\right)} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}}, -1, -1\right) \]

      10. +-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{z \cdot \cos y + \sin y}}{x}, -1, -1\right) \]

      11. *-commutative N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\cos y \cdot z} + \sin y}{x}, -1, -1\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)}}{x}, -1, -1\right) \]

      13. lower-cos.f64 N/A

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right)}{x}, -1, -1\right) \]

      14. lower-sin.f64 98.2

          \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right)}{x}, -1, -1\right) \]

   7. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\cos y, z, \sin y\right)}{x}, -1, -1\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{z \cdot \cos y}{x}, -1, -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 95.9%

       \[\leadsto \left(-x\right) \cdot \mathsf{fma}\left(\frac{\cos y \cdot z}{x}, -1, -1\right) \]

   if -520 < z < 3.80000000000000026e-24

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 100.0

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, z, \sin y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, z, \sin y + x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;x \leq -3.2:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-305}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= x -3.2)
     (+ z x)
     (if (<= x -2.6e-197)
       t_0
       (if (<= x 1.25e-305)
         (fma 1.0 z (sin y))
         (if (<= x 2.6e-49) t_0 (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (x <= -3.2) {
		tmp = z + x;
	} else if (x <= -2.6e-197) {
		tmp = t_0;
	} else if (x <= 1.25e-305) {
		tmp = fma(1.0, z, sin(y));
	} else if (x <= 2.6e-49) {
		tmp = t_0;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (x <= -3.2)
		tmp = Float64(z + x);
	elseif (x <= -2.6e-197)
		tmp = t_0;
	elseif (x <= 1.25e-305)
		tmp = fma(1.0, z, sin(y));
	elseif (x <= 2.6e-49)
		tmp = t_0;
	else
		tmp = Float64(z + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -3.2], N[(z + x), $MachinePrecision], If[LessEqual[x, -2.6e-197], t$95$0, If[LessEqual[x, 1.25e-305], N[(1.0 * z + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-49], t$95$0, N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2000000000000002 or 2.59999999999999995e-49 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z + x} \]

      2. lower-+.f64 87.1

         \[\leadsto \color{blue}{z + x} \]

   5. Applied rewrites 87.1%

      \[\leadsto \color{blue}{z + x} \]

   if -3.2000000000000002 < x < -2.6000000000000001e-197 or 1.24999999999999996e-305 < x < 2.59999999999999995e-49

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.8

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 71.0

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -2.6000000000000001e-197 < x < 1.24999999999999996e-305

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \sin y \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]

      4. lower-cos.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right) \]

      5. lower-sin.f64 99.9

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right) \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(1, z, \sin y\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 87.2%

      \[\leadsto \mathsf{fma}\left(1, z, \sin y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-305}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+169} \lor \neg \left(z \leq 1.18 \cdot 10^{+116}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e+169) (not (<= z 1.18e+116)))
   (* (cos y) z)
   (fma 1.0 z (+ (sin y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+169) || !(z <= 1.18e+116)) {
		tmp = cos(y) * z;
	} else {
		tmp = fma(1.0, z, (sin(y) + x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e+169) || !(z <= 1.18e+116))
		tmp = Float64(cos(y) * z);
	else
		tmp = fma(1.0, z, Float64(sin(y) + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e+169], N[Not[LessEqual[z, 1.18e+116]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(1.0 * z + N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999995e169 or 1.1799999999999999e116 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.8

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 94.4

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 94.4%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -6.4999999999999995e169 < z < 1.1799999999999999e116

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.9

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, z, \sin y + x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 90.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1}, z, \sin y + x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+169} \lor \neg \left(z \leq 1.18 \cdot 10^{+116}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \sin y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+169} \lor \neg \left(z \leq 1.18 \cdot 10^{+116}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.5e+169) (not (<= z 1.18e+116))) (* (cos y) z) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+169) || !(z <= 1.18e+116)) {
		tmp = cos(y) * z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-6.5d+169)) .or. (.not. (z <= 1.18d+116))) then
        tmp = cos(y) * z
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.5e+169) || !(z <= 1.18e+116)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.5e+169) or not (z <= 1.18e+116):
		tmp = math.cos(y) * z
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.5e+169) || !(z <= 1.18e+116))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.5e+169) || ~((z <= 1.18e+116)))
		tmp = cos(y) * z;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.5e+169], N[Not[LessEqual[z, 1.18e+116]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999995e169 or 1.1799999999999999e116 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x + \sin y\right) + z \cdot \cos y} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \cos y + \left(x + \sin y\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \cos y} + \left(x + \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} + \left(x + \sin y\right) \]

      5. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{x + \sin y}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

      8. lower-+.f64 99.8

         \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y + x}\right) \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y + x\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\cos y \cdot z} \]

      3. lower-cos.f64 94.4

         \[\leadsto \color{blue}{\cos y} \cdot z \]

   7. Applied rewrites 94.4%

      \[\leadsto \color{blue}{\cos y \cdot z} \]

   if -6.4999999999999995e169 < z < 1.1799999999999999e116

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{z + x} \]

      2. lower-+.f64 73.4

         \[\leadsto \color{blue}{z + x} \]

   5. Applied rewrites 73.4%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+169} \lor \neg \left(z \leq 1.18 \cdot 10^{+116}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z x))

C

double code(double x, double y, double z) {
	return z + x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + x
end function

Java

public static double code(double x, double y, double z) {
	return z + x;
}

Python

def code(x, y, z):
	return z + x

Julia

function code(x, y, z)
	return Float64(z + x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + x;
end

Wolfram

code[x_, y_, z_] := N[(z + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x + z} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{z + x} \]

   2. lower-+.f64 66.9

      \[\leadsto \color{blue}{z + x} \]

5. Applied rewrites 66.9%

   \[\leadsto \color{blue}{z + x} \]

6. Final simplification 66.9%

   \[\leadsto z + x \]
7. Add Preprocessing

Alternative 9: 29.9% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ z + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z y))

C

double code(double x, double y, double z) {
	return z + y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + y
end function

Java

public static double code(double x, double y, double z) {
	return z + y;
}

Python

def code(x, y, z):
	return z + y

Julia

function code(x, y, z)
	return Float64(z + y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + y;
end

Wolfram

code[x_, y_, z_] := N[(z + y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\cos y \cdot z} + \sin y \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]

   4. lower-cos.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\cos y}, z, \sin y\right) \]

   5. lower-sin.f64 56.1

      \[\leadsto \mathsf{fma}\left(\cos y, z, \color{blue}{\sin y}\right) \]

5. Applied rewrites 56.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, \sin y\right)} \]

6. Taylor expanded in y around 0

   \[\leadsto y + \color{blue}{z} \]
7. Step-by-step derivation

8. Applied rewrites 25.0%

   \[\leadsto z + \color{blue}{y} \]

9. Final simplification 25.0%

   \[\leadsto z + y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))